An a posteriori error estimator for the weak Galerkin least-squares finite-element method

被引：9

作者：

Adler, James H. ^{[1
]}

Hu, Xiaozhe ^{[1
]}

Mu, Lin ^{[2
]}

Ye, Xiu ^{[3
]}

机构：

[1] Tufts Univ, Dept Math, Medford, MA 02155 USA

[2] Oak Ridge Natl Lab, Comp Sci & Math Div, Oak Ridge, TN 37831 USA

[3] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 362卷

基金：

美国国家科学基金会;

关键词：

Weak Galerkin; Finite-element methods; Least-squares finite-element methods; Second-order elliptic problems; APPROXIMATION; ALGORITHM;

D O I：

10.1016/j.cam.2018.09.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive an a posteriori error estimator for the weak Galerkin least squares (WG-LS) method applied to the reaction-diffusion equation. We show that this estimator is both reliable and efficient, allowing it to be used for adaptive refinement. Due to the flexibility of the WG-LS discretization, we are able to design a simple and straightforward refinement scheme that is applicable to any shape regular polygonal mesh. Finally, we present numerical experiments that confirm the effectiveness of the estimator, and demonstrate the robustness and efficiency of the proposed adaptive WG-LS approach. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：383 / 399

页数：17

共 35 条

[1] EFFICIENCY BASED ADAPTIVE LOCAL REFINEMENT FOR FIRST-ORDER SYSTEM LEAST-SQUARES FORMULATIONS [J].

Adler, J. H. ;

Manteuffel, T. A. ;

McCormick, S. F. ;

Nolting, J. W. ;

Ruge, J. W. ;

Tang, L. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2011, 33 (01) :1-24

[2]

[Anonymous], 1995, A Review of A Posteriori Error Estimation and Adaptive Mesh Refinement Techniques

[3]

Bank R. E., 2003, SIAM Review, V45, P291, DOI 10.1137/S003614450342061

[4] ANALYSIS OF LEAST-SQUARES FINITE-ELEMENT METHODS FOR THE STOKES EQUATIONS [J].

BOCHEV, PB ;

GUNZBURGER, MD .

MATHEMATICS OF COMPUTATION, 1994, 63 (208) :479-506

[5] ACCURACY OF LEAST-SQUARES METHODS FOR THE NAVIER-STOKES EQUATIONS [J].

BOCHEV, PB ;

GUNZBURGER, MD .

COMPUTERS & FLUIDS, 1993, 22 (4-5) :549-563

[6] A least-squares approach based on a discrete minus one inner product for first order systems [J].

Bramble, JH ;

Lazarov, RD ;

Pasciak, JE .

MATHEMATICS OF COMPUTATION, 1997, 66 (219) :935-955

[7] 1ST-ORDER SYSTEM LEAST-SQUARES FOR 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS .1. [J].

CAI, Z ;

LAZAROV, R ;

MANTEUFFEL, TA ;

MCCORMICK, SF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (06) :1785-1799

[8] First-order system least squares for second-order partial differential equations .2. [J].

Cai, ZQ ;

Manteuffel, TA ;

McCormick, SF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (02) :425-454

[9]

Cai ZQ, 2000, NUMER METH PART D E, V16, P62

[10]

Cai ZQ, 1999, NUMER LINEAR ALGEBR, V6, P479, DOI 10.1002/(SICI)1099-1506(199909)6:6<479::AID-NLA172>3.0.CO

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